Synchronous Vibration Parameter Recognition of Constant-Speed Blades Based on Blade Tip Clearance Measurement
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe subject addressed is new and has interest.
The work is clearly laid out.
The description of the methodology is inadequate.
The numerical model is not described.
The experimental model should be better described.
The results should be better presented.
The conclusions are supported in the presented results.
I suggest the following improvements:
- The description of figure 1 is not adequate: the meaning of some of the parameters (for example TIPj, βj) is not understandable and other parameters are only defined at the end of section 2; the positioning of the blade is not explained; it is not possible to distinguish the objective of representations a) and b).
- It seems to me that the model formulation would be simplified using polar coordinates instead of Cartezian coordinates (x,y).
- In aero-engine compressor and turbine, the axial thrust causes axial deformation of the blade; In the present study, this deformation is not taken into account, and this simplification and the error it would cause in the model are not justified.
- Equations 4 and 5 do not appear in the manuscript, making understanding the model practically impossible.
- In section 3, in the simulation, the values adopted for the variables or parameters, namely the sensor mounting angles, are not reasoned; Also the introduced “measured values of the BTC sensors” are not specified.
- In section 4, the experimental setup and results presented are not adequately described.
- The title of section 6 (6. Patents) must be deleted.
Comments on the Quality of English LanguageThe language should be polished to improve the quality of the manuscript.
Author Response
Dear Editors and Reviewers,
Thank you very much for your letter and for the reviewers' comments concerning our manuscript entitled " Synchronous Vibration Parameters Recognition of Constant Speed Blade based on Blade Tip Clearance Measurement" (ID: applsci-2740059) Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. The main corrections in the manuscript and the responds to the reviewer’s comments are listed as follows. The corrections parts in the manuscript are marked in blue.
Reviewer 1
The subject addressed is new and has interest.
The work is clearly laid out.
The description of the methodology is inadequate.
The numerical model is not described.
The experimental model should be better described.
The results should be better presented.
The conclusions are supported in the presented results.
Response: Thanks for your advice, the methodology, numerical model, experimental model and results have been better described in the manuscript.
Comment 1: The description of figure 1 is not adequate: the meaning of some of the parameters (for example TIPj, βj) is not understandable and other parameters are only defined at the end of section 2; the positioning of the blade is not explained; it is not possible to distinguish the objective of representations a) and b).
Response: Thanks for your suggestion. Figure 1 is explained in more detail in the manuscript. The purpose of distinguishing (a and (b is explained, and the two graphs of (a and (b are distinguished and explained.
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(a) |
(b) |
In Fig.1,(a) is the geometric model between BTC and BTVD when the blade tip arrives early, ( b ) is the geometric model between BTC and BTVD when the blade tip arrives late. According to the different arrival states of the blade, we will choose different models and formulas.
The serial number of the sensor is set to 0, 1, 2,..., n-1, that is, the sensor TIPj ( j = 0, 1..., n-1 ). The installation angle of each sensor relative to the Tip0 sensor is , , ... (), that is, the installation angle of the sensor j relative to the Tip0 sensor ( j = 0, 1..., n-1 ). is the vibration angle of the blade tip when the blade tip passes through the TIPj. is the static blade. is the deformed blade. R is the distance between the probe of the BTC measurement sensor and the rotation axis. e is the radius of the blade-disc. and , are the deformation of blade tip in x direction and y direction respectively. is the tip vibration displacement(BTVD). is deformation angle of the blade.
Comment 2:It seems to me that the model formulation would be simplified using polar coordinates instead of Cartezian coordinates (x,y).
Response:Thanks to your comments, We think your suggestion is very valuable. Using polar coordinates to simplify the model formula is a good idea, but the modification of the model formula is related to a lot of follow-up work, which is difficult to complete in a short time. In the follow-up study, we will try.
Comment 3: In aero-engine compressor and turbine, the axial thrust causes axial deformation of the blade; In the present study, this deformation is not taken into account, and this simplification and the error it would cause in the model are not justified.
Response: Thanks for your suggestion. We think your suggestion is very valuable. Since this paper mainly studies the constant speed synchronous vibration of low pressure compressor ( low temperature ) blade, only the constant deformation and vibration deformation of blade under aerodynamic force and the deformation of rotor under centrifugal force are considered. We have added relevant content. In the future, we will continue to deepen our research and continue to analyze various types of leaf deformation.
Comment 4: Equations 4 and 5 do not appear in the manuscript, making understanding the model practically impossible.
Response: The missing formulas have been added.
Equations 4:
Equations 5:
Comment 5: In section 3, in the simulation, the values adopted for the variables or parameters, namely the sensor mounting angles, are not reasoned; Also the introduced “measured values of the BTC sensors” are not specified.
Response: Thanks for your suggestion. We give a more detailed description of 'measured values of the BTC sensors '. In the future, we will continue to study the installation angle, and now the sensor mounting angles we mainly refer to this paper:
Ouyang, T. Rotating Blade Vibration Detection and Parameters recognition Technique Using Blade Tip-Timing,PHD,Tianjin University, tianjin,. 2011.
Comment 6: In section 4, the experimental setup and results presented are not adequately described.
Response: The setup and results of section 4 have been described more fully:
Setup: In order to verify the feasibility of the approach, a vertical axis integrated blade rotary table was used in this experiment, the speed of the blade is controlled by a servo motor. The data collector collects the voltage changes perceived by the blade tip when it passes through the sensor and processes them to obtain BTC. When the integrated blade with a blade length of 40 mm and a disc radius of 40 mm works at a speed of 3000 rpm, four BTC sensors and a speed sensor are used for monitoring. The installation angles of the four BTC sensors are 0°, 15°, 29°and 43°.
Results: The above data show that the method can identify the synchronous vibration parameters of the constant speed rotating linear blade, and the identified vibration parameters are within a reasonable range. When using this method, we need to get the deformation of the blade in advance. Limited by the experimental equipment, we can not obtain the deformation of the actual blade. Therefore, we obtain the deformation of the blade by calculation. If the deformation of the actual blade can be obtained, the method proposed in this paper can obtain more accurate identification results. Therefore, the vibration parameter identification method proposed in this paper is feasible in the synchronous vibration parameter identification of blade with constant speed.
Comment 7: The title of section 6 (6. Patents) must be deleted.
Response: Section 6 has been deleted.
Finally, we appreciate for Editors/Reviewers' warm work earnestly, and hope that the correction will meet with approval. Once again, thank you very much for your comments and suggestions.
Best regards,
Liang Zhang, Yiming Xia, Cong Chen, Qingxi Song and Junjun Cao
Address: 169 Shiying Street, Guta District, Jinzhou City, Liaoning Province, China. Faculty of Mechanical Engineering and Automation. Liaoning University of Technology.
Phone: +8615941611803
E-mail address: [email protected]
December 8, 2023
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsDear Authors,
1) Purpose of the research: determining the parameters of synchronous vibrations using the blade tip clearance (BTC) to blade tip clearance (BTVD) transformation method using the additional blade tip timing (BTT) method - presenting an outline of the new method proposal.
2) Each new approach aimed at improving such an important problem (in various respects) is worth testing and reviewing, especially when the presented assumptions already indicate such validity.
3) The proposed method explicitly presents a model of the process of determining vibration displacemets (in other methods this process was conducted indirectly, e.g. using a developed dynamic model (differential equations) or FEM - it is a pity that the authors did not mention these and still other ways of determining BTVD
4) Indeed, the current method is very simplified, if only because it takes into account only one and the simplest (but probably the most common) case of turbine blade deformation. Here, the authors should cite the paper which presents 5 basic cases of blade deflection and deplanation:
Xulong Zhang, Weimin Wang, Kang Chen, Weibo Li, Dengpeng Zhang, Linlin Tian. Five dimensional movement measurement method for rotating blade based on blade tip timing measuring point position tracking. Mechanical Systems and Signal Processing 161 (2021) 107898
5) The conclusions resulting from the obtained research results should be slightly extended, although a more detailed justification of the derivation and/or use of some calculation formulas, graphical models, a closer explanation of the experiment is much more important - the lack of the most important parameter (according to some researchers), which is rotational speeds, one in short, the manuscript is very unfriendly
6) There are significant gaps in references - there is a complete lack of citations to papers regarding the main method, i.e. BTVD, e.g.:
Mohamed Mohamed, Philip Bonello, Peter Russhard: A novel method for the determination of the change in blade tip timing probe sensing position due to steady movements. Mechanical Systems and Signal Processing 126 (2019) 686–710
7) In this type of research using very accurate sensors, continuous (analog) waveforms are obtained, e.g. of displacements. The Authors present sensor data in tables discreetly
8) Other important notes
a) Row 116 - not cite the literature on BTT, preferably the Authors' own previous paper, where the derivation of the dependencies for this auxiliary method is presented in a natural way (only a few formulas are listed in the assessed manuscript, and without explanation of important parameters, e.g. x*1, y*1 (formulas (17), (18):
Liang Zhang, Qidi Wang and Xin Li Vibration. Parameters Identification of Rotating Blades Based on Blade Tip-Timing Sensor Waveforms. Appl. Sci. 2023, 13, 5920. https://doi.org/10.3390/app13105920
and:
Bing Yu, Hongwei Ke, Enyu Shen and Tianhong Zhang. A review of blade tip clearance– measuring technologies for gas turbine engines. Measurement and Control 53(3-4).
CraigP. Lawson, Paul C. Ivey. Turbomachinery Blade Vibration Amplitude Measurement Through Tip Timing with Capacitance Tip Clearance Probes. January 2005 Sensors and Actuators A Physical 118(1):14-24
b) Row Missing formulas 4 and 5,
c) Rows 187, 211, 239, … , no data markings entered, only units - mm, are listed,
d) It is rare to find papers in the main part of which there are no citations at all, which makes studying very difficult and gives the impression that the author(s) are the originators of the entire theory and applications of the theory.
9). Future directions:
a) The authors should conduct research at several rotational speeds so that a Campbell diagram can be constructed to determine the natural frequency and the danger of resonance - this is becoming a standard,
b) The authors also should pay attention to the need to conduct uncertain analysis. Such an analysis is carried out when the measurement results are subject to random errors (due to, for example, the influence of centrifugal forces on the measurement results, blade wear and temperature, or the placement of sensors). Then, probabilistic analysis or analysis using rough sets or fuzzy sets or Monte Carlo simulation could be performed. Most often, however, simple statistical analysis is enough.
The implementation of these few, not very time-consuming comments should allow the authors to prepare a much more valuable paper (according to the reviewer).
Best regards, Reviewer.
Comments for author File: Comments.pdf
I am not very qualified to assess the quality of English in this paper. In any case, I found it very difficult to read.
Author Response
Dear Editors and Reviewers,
Thank you very much for your letter and for the reviewers' comments concerning our manuscript entitled " Synchronous Vibration Parameters Recognition of Constant Speed Blade based on Blade Tip Clearance Measurement" (ID: applsci-2740059) Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. The main corrections in the manuscript and the responds to the reviewer’s comments are listed as follows. The corrections parts in the manuscript are marked in blue.
Reviewer 2
Comment 1: Purpose of the research: determining the parameters of synchronous vibrations using the blade tip clearance (BTC) to blade tip clearance (BTVD) transformation method using the additional blade tip timing (BTT) method - presenting an outline of the new method proposal.
Response: Thanks to your comments, this manuscript adds a research outline.
Row105~106: Purpose of the research: determining the parameters of synchronous vibrations using the BTC to BTVD transformation method using the additional BTT method.
Comment 2: Each new approach aimed at improving such an important problem (in various respects) is worth testing and reviewing, especially when the presented assumptions already indicate such validity.
Response: Thanks to your comments. We will continue to deepen our research, continue to analyze and test more aspects, and gradually improve this method.
Comment 3: The proposed method explicitly presents a model of the process of determining vibration displacemets (in other methods this process was conducted indirectly, e.g. using a developed dynamic model (differential equations) or FEM - it is a pity that the authors did not mention these and still other ways of determining BTVD
Response: Thanks to your comments,we added about BTVD in the manuscript.
Row101~104: BTVD is usually obtained by processing the time series, and the time series of the tip arrival is obtained by the BTT sensor. But in this paper, the BTVD is obtained by using the ( BTC ) to ( BTVD ) conversion method. The sensor obtains the time series of BCT rather than tip arrival.
Comment 4: Indeed, the current method is very simplified, if only because it takes into account only one and the simplest (but probably the most common) case of turbine blade deformation. Here, the authors should cite the paper which presents 5 basic cases of blade deflection and deplanation:
Xulong Zhang, Weimin Wang, Kang Chen, Weibo Li, Dengpeng Zhang, Linlin Tian. Five dimensional movement measurement method for rotating blade based on blade tip timing measuring point position tracking. Mechanical Systems and Signal Processing 161 (2021) 107898
Response: Thanks to your comments. We think this paper is very valuable. Has been cited as a reference:
[25]Zhang, X.; Wang, W.; Chen, K.; Li, W.; Zhang, D.; Tian, L. Five dimensional movement measurement method for rotating blade based on blade tip timing measuring point position tracking. Mechanical Systems and Signal Processing 2021, 161, 107898.
Comment 5: The conclusions resulting from the obtained research results should be slightly extended, although a more detailed justification of the derivation and/or use of some calculation formulas, graphical models, a closer explanation of the experiment is much more important - the lack of the most important parameter (according to some researchers), which is rotational speeds, one in short, the manuscript is very unfriendly
Response: We think this comment is very valuable. This paper extends the conclusions of the research results. Experimental parameters such as speed are added.
Conclusions: In this paper, a new method for synchronous vibration parameters of constant speed rotating blades based on BTC measurement is proposed. By establishing a geometric model between BTC and BTVD, BTC is associated with BTVD. Through the existing BTC monitoring method, the BTC of the blade tip passing through each sensor is obtained. The BTT method is used to determine whether the blade tip arrives in advance or in lag time, and then the geometric model is used to obtain BTVD. Finally, the nonlinear least squares method is used to identify the synchronous vibration parameters of the constant speed rotating blade. And the identification accuracy of the method is verified by numerical simulation. The conclusions are as follows : With the increase of vibration amplitude, the random error of blade disc size and BTC measurement decreases, and the vibration parameter identification accuracy of this method is higher. The smaller the ratio of blade length to disk radius is, the higher the accuracy of the vibration parameter identification method introduced in this paper is. Since the compressor and turbine blade disk structures are small r/e ratio structure, the method proposed in this paper is suitable for the identification of synchronous vibration parameters of compressor blades and turbine blades. In the future, we will analyze the uncertain factors such as temperature and centrifugal force measurement at different speeds, and carry out statistical analysis to gradually improve this method. With the development of BTC measurement method and our research, the recognition accuracy of this method will also be improved. This method will be applicable to all rotating blade vibration parameter identification.
Experimental parameters: In order to verify the feasibility of this method, the vertical axis integrated blade turntable is used in this experiment, as shown in Fig.21. The speed of the blade is controlled by a servo motor. The data collector collects the voltage changes perceived by the blade tip when it passes through the sensor and processes them to obtain BTC. When the integrated blade with a blade length of 40 mm and a disc radius of 40 mm works at a speed of 3000 rpm, four BTC sensors and a speed sensor are used for monitoring. The installation angles of the four BTC sensors are 0°,15°,29°,43°.
Comment 6: There are significant gaps in references - there is a complete lack of citations to papers regarding the main method, i.e. BTVD, e.g.:Mohamed Mohamed, Philip Bonello, Peter Russhard: A novel method for the determination of the change in blade tip timing probe sensing position due to steady movements. Mechanical Systems and Signal Processing 126 (2019) 686–710
Response: Thanks to your comments. We think this paper is valuable. It has been cited with more BTVD-related literature as a reference.
[28]Mohamed, M.; Bonello, P.; Russhard, P. A novel method for the determination of the change in blade tip timing probe sensing position due to steady movements. Mechanical Systems and Signal Processing 2019, 126, 686-710.
[29]Ren, S.; Xiang, X.; Zhao, W.; Zhao, Q.; Wang, C.; Xu, Q. An error correction blade tip-timing method to improve the measured accuracy of blade vibration displacement during unstable rotation speed. Mechanical Systems and Signal Processing 2022, 162, 108030.
[30]Meiru LIU, G.T., XIAO Xiao. Vibration measurement of turbine rotor blades of aero-engine based on blade tip-timing. Journal of Aerospace Power 2020, 9.
[31]MENG Yiming, X.Z., OUYANG Hua. High-accuracy experimental analysis and correction of blade tip timing measurement error. Journal of Aerospace Power 2023, 39, 1-12.
Comment 7: In this type of research using very accurate sensors, continuous (analog) waveforms are obtained, e.g. of displacements. The Authors present sensor data in tables discreetly
Response: Thanks to your comments,we have added the blade arrival information to the Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8.
Comment 8a: Row 116 - not cite the literature on BTT, preferably the Authors' own previous paper, where the derivation of the dependencies for this auxiliary method is presented in a natural way (only a few formulas are listed in the assessed manuscript, and without explanation of important parameters, e.g. x*1, y*1 (formulas (17), (18):Liang Zhang, Qidi Wang and Xin Li Vibration. Parameters Identification of Rotating Blades Based on Blade Tip-Timing Sensor Waveforms. Appl. Sci. 2023, 13, 5920. https://doi.org/10.3390/app13105920
and:
Bing Yu, Hongwei Ke, Enyu Shen and Tianhong Zhang. A review of blade tip clearance– measuring technologies for gas turbine engines. Measurement and Control 53(3-4).
CraigP. Lawson, Paul C. Ivey. Turbomachinery Blade Vibration Amplitude Measurement Through Tip Timing with Capacitance Tip Clearance Probes. January 2005 Sensors and Actuators A Physical 118(1):14-24
Response: Thanks to your comments. We explained the relevant parameters. We explain the relevant parameters. And think these three articles are very valuable. has been cited as a reference.
Row200：where x1 is the first row of the solution vector and x2 is the second row of the solution vector
[32]Liang, Z.; Qidi, W.; Xin, L. Vibration Parameters Identification of Rotating Blades Based on Blade Tip-Timing Sensor Waveforms. Applied Sciences 2023, 13, 5920.
[33]Lawson, C.; Ivey, P. Tubomachinery blade vibration amplitude measurement through tip timing with capacitance tip clearance probes. Sensors and Actuators A: Physical 2005.
[34]Yu, B.; Ke, H.; Shen, E.; Zhang, T. A review of blade tip clearance–measuring technologies for gas turbine engines. Measurement and Control -London- Institute of Measurement and Control- 2020, 53, 002029401987751.
Comment 8b: Row Missing formulas 4 and 5,
Response: The missing formulas have been added
Formulas 4:
Formulas 5:
Comment 8c: Rows 187, 211, 239, … , no data markings entered, only units - mm, are listed,
Response: The missing data have been added.
Original row187: When the blade length r=50mm, blade-disk radius e=150mm, and the distance between the BTC sensor and the rotation axis R=202mm.
Original row211: When the blade length r=100mm, blade-disk radius e=100mm, and the distance between the BTC sensor and the rotation axis R=202mm.
Original row239: When the blade length r=150mm, blade-disk radius e=50mm, and the distance between the BTC sensor and the rotation axis R=202mm.
Comment 8d: It is rare to find papers in the main part of which there are no citations at all, which makes studying very difficult and gives the impression that the author(s) are the originators of the entire theory and applications of the theory.
Response: Thanks to your comments. We add more references in the main part of the thesis to make it easier to read.
[32] Liang, Z.; Qidi, W.; Xin, L. Vibration Parameters Identification of Rotating Blades Based on Blade Tip-Timing Sensor Waveforms. Applied Sciences 2023, 13, 5920.
[33] Lawson, C.; Ivey, P. Tubomachinery blade vibration amplitude measurement through tip timing with capacitance tip clearance probes. Sensors and Actuators A: Physical 2005.
[34]Yu, B.; Ke, H.; Shen, E.; Zhang, T. A review of blade tip clearance–measuring technologies for gas turbine engines. Measurement and Control -London- Institute of Measurement and Control- 2020, 53, 002029401987751.
[35] Rigosi, G.; Battiato, G.; Berruti, T.M. Synchronous vibration parameters identification by tip timing measurements. Mechanics Research Communications 2017, 79, 7-14, doi:https://doi.org/10.1016/j.mechrescom.2016.10.006.
[36]Ouyang, T. Rotating Blade Vibration Detection and Parameters Identification Technique Using Blade Tip-Timing,PHD,Tianjin University, tianjin,. 2011(05).
Comment 9a: The authors should conduct research at several rotational speeds so that a Campbell diagram can be constructed to determine the natural frequency and the danger of resonance - this is becoming a standard,
Response: Thanks to your comments. We think your suggestion is very valuable. Our idea is the same as yours. Our thoughts are the same as yours. My colleague is doing related research, which may be seen in other papers in the future.
Comment 9b: The authors also should pay attention to the need to conduct uncertain analysis. Such an analysis is carried out when the measurement results are subject to random errors (due to, for example, the influence of centrifugal forces on the measurement results, blade wear and temperature, or the placement of sensors). Then, probabilistic analysis or analysis using rough sets or fuzzy sets or Monte Carlo simulation could be performed. Most often, however, simple statistical analysis is enough.
Response: Thanks to your comments. We think your suggestions are very valuable, and we will do more research under your suggestions in the future.
Finally, we appreciate for Editors/Reviewers' warm work earnestly, and hope that the correction will meet with approval. Once again, thank you very much for your comments and suggestions.
Best regards,
Liang Zhang, Yiming Xia, Cong Chen, Qingxi Song and Junjun Cao
Address: 169 Shiying Street, Guta District, Jinzhou City, Liaoning Province, China. Faculty of Mechanical Engineering and Automation. Liaoning University of Technology.
Phone: +8615941611803
E-mail address: [email protected]
December 8, 2023
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAll my doubts were adequately clarified.
Thank you.
Reviewer 2 Report
Comments and Suggestions for AuthorsDear Authors
Thank you very much for your detailed response to my review. After taking into account the comments, the paper became much more pleasant to read and easier to understand. It is a pity that the Authors did not mention that the analyzed case of turbine blade deformation is only one of the possible cases.
Kind Regards Reviewer
